Humans are the only animal to use numbers-- at least exact numbers such as 2007 or even seven. We share with other species the ability to perceive small, exact numbers such as one, two, and three, and also to perceive large, approximate numbers such as 'about 50,' as opposed to 'about 25' or 'about 100.' But only humans use numbers that are both large and exact-- numbers such as 5, 6, 7,. . . etc. Humans are also the only animal to use language, and thus to create external, linguistic symbols for numbers. Because children learn to speak before they learn to read, the first linguistic number symbols they learn are the number words: "One," "two," "three," . . . etc. This research asks how the mental symbols (the number concepts) are related to the linguistic symbols (the number words). Are number words just handy labels for ideas of 5, 6, 7, and so forth that humans are born with? Or are number concepts themselves a cultural invention that gets passed down from generation to generation? This research aims to answer two very basic questions. First, when a child learns the meaning of a number word such as "two" or "five," does the child construct a concept of 'twoness' or 'fiveness' that she didn't have before? Or does she simply learn a label for a concept of 'twoness' or 'fiveness' that was already there? Second, are the meanings of number words learned gradually (as we might expect if the number concept itself is being constructed), or are they learned all at once (as we might expect if the child already has the concept)? Specifically, this research has two aims. Aim 1 is to determine whether number-word learning actually means constructing new number concepts, or simply learning new labels for old concepts. For example, Study 1 will determine whether children's attention and memory for small numbers improves after they learn the word for that number. Study 2 will determine whether learning a particular number word makes that number available as a candidate meaning for new quantity terms like "a couple," "a few," and "both." Study 3 will determine when children understand that one- to-one correspondence is the basis for numbers. This means that any set of, for example, five items can be matched up one-to-one with any other set of five items, without having any items left over. Aim 2 is to identify early steps in number-word learning. If children are constructing number concepts in the process of learning number-word meanings, then it is reasonable to expect that they will grasp some aspects of the meaning before others. Study 4 will tell us when children learn that number-words apply to discrete quantification rather than continuous quantification. For example, you can have "five buttons" but not "five sand." Study 5 will tell us when children learn that number words refer to a property of sets rather than a property of individuals. For example, green is a property of an individual turtle, but five is a property of a set of turtles. [unreadable] [unreadable] [unreadable]